GUADALAJARA, Mexico (Reuters) - The leftist front-runner for the Mexican presidency softened his critical stance on Mexico City's $13 billion new airport on Friday, saying he would carefully review the project instead of threatening to scrap it entirely.

Speaking in the central city of Guadalajara, Andres Manuel Lopez Obrador, who has led polls for months ahead of the July 1 election, stressed the need to examine all aspects of the project, which is already under construction.

"We are going to do a technical review of the project, without scaring anyone," he said at a construction industry conference in Mexico's second-biggest city.

"(Hold) a review, with all honesty as to whether it goes ahead or it doesn't; those are the options," he added.

Lopez Obrador proposed assembling a team of 15 experts to assess the project - five from the construction industry, five from the government and five from his team.

It was a more conciliatory stance than his remarks on Thursday, when he said his legal team would file injunctions to block the government from awarding more work contracts for the project, which he slammed as "corrupt."

His pick for communications and transport minister, Javier Jimenez Espriu, told the conference that if elected, Lopez Obrador would suspend work to conduct a financial, environmental and technical review to assess the project's full impact.

"We are not for having white elephants," Espriu said.

Contracts worth billions of dollars have already been awarded for the airport, which aims to ease the strained capacity of the capital's present hub and improve connectivity.

The largest existing contract went to a consortium that includes a construction company controlled by Mexican tycoon Carlos Slim, one of the world's richest men.

Ricardo Anaya, a rival presidential candidate heading a right-left coalition who is battling for second place in the race, said it would be foolish to scrap the airport, given the amount of money already assigned to the project.

But he also called for it to be subject to scrutiny.

"What we do need to do is review the contracts to guarantee that this project is being carried out to the highest international standards of transparency, and that it's not being used for corruption," he told the same construction event.

Mexico's airlines' chamber Canaero said in a statement that it was firmly against the Lopez Obrador plan to assess the viability of the airport, as scrapping the project would limit connectivity, raise airlines' costs and hamper their operations, while also affecting passengers.

"The viability of this project is not up for discussion," it said, adding that the project "is indispensable for the future of Mexico."

The project, which is being built on the drained bed of Lake Texcoco, is the biggest public works project under way in Mexico. The planned terminal building was designed by British architect Norman Foster and Slim's son-in-law, Fernando Romero.

GACM, the company responsible for building the airport, said on Friday that it had raised 30 billion pesos ($1.62 billion) through an offering of an infrastructure investment trust to help finance the project.